The WTP/WTA Disparity: Have We Been Observing
Dynamic Values but Interpreting Them as Static?
Catherine L. Kling, John A. List, and Jinhua Zhao
Working Paper 03-WP 333
May 2003
Center for Agricultural and Rural Development
Iowa State University
Ames, Iowa 50011-1070
www.card.iastate.edu
Catherine Kling is a professor in the Department of Economics and Center for Agricultural and
Rural Development, Iowa State University. She was a visiting researcher at the Institut National
de Recherche Agronomique (INRA), University of Toulouse, Paris, when this paper was written.
John List is a senior economist with the Council of Economic Advisers, a faculty research fellow
with the National Bureau of Economic Research, and a professor of economics at the University
of Maryland. Jinhua Zhao is an assistant professor in the Department of Economics, Iowa State
University. Glenn Harrison, Danny Kahneman, and Bob Sugden provided useful remarks. The
authors thank seminar participants at several universities and conferences for providing useful
comments. Any remaining errors are those of the authors.
This publication is available online on the CARD website: www.card.iastate.edu. Permission is
granted to reproduce this information with appropriate attribution to the authors and the Center for
Agricultural and Rural Development, Iowa State University, Ames, Iowa 50011-1070.
For questions or comments about the contents of this paper, please contact Cathy Kling, 578
Heady Hall, Iowa State University, Ames, IA 50011-1070; Ph: 515-294-5767; Fax: 515-294-6336;
E-mail: ckling@iastate.edu.
Iowa State University does not discriminate on the basis of race, color, age, religion, national origin, sexual
orientation, sex, marital status, disability, or status as a U.S. Vietnam Era Veteran. Any persons having
inquiries concerning this may contact the Director of Equal Opportunity and Diversity, 1350 Beardshear Hall,
515-294-7612.
Abstract
This study advances, and experimentally tests, a new explanation for the disparity
between willingness to pay (WTP) and willingness to accept (WTA)—a dynamic
neoclassical theory based on the presence of commitment costs. While to date
neoclassical models have not explained the observed data patterns well, we find that the
commitment cost theory is able to explain adequately the causes and severity of the
WTP/WTA value disparity. In particular, using data gathered from an actual marketplace,
even the most stringent of our theoretical conjectures—cases where WTP values are
predicted to exceed WTA values—oftentimes are met.
Keywords: field experiment, neoclassical theory, willingness to accept, willingness to
pay, WTP/WTA disparity.
JEL: Q21, Q26
THE WTP/WTA DISPARITY: HAVE WE BEEN OBSERVING
DYNAMIC VALUES BUT INTERPRETING THEM AS STATIC?
A fundamental tenet in neoclassical theory is the basic independence assumption: an
individual’s preferences are assumed to be measured over levels, not over changes. While
most theoretical and applied economic models invoke this assumption, a wealth of data
refutes this premise, as systemic empirical disparities have been observed between
willingness to pay (WTP) and the compensation demanded, or willingness to accept
(WTA), for the same good (e.g., Kahneman, Knetsch, and Thaler 1990). In an influential
line of work, Hanemann (1991) shows that the large WTP/WTA disparities that have
been observed in the literature can be reconciled with static neoclassical theory via
income and substitution effects, but the empirical evidence to date has not conformed
well to Hanemann’s (1991), or any other, neoclassical-based model.1 If the disparity is
inconsistent with neoclassical explanations, then there are profound implications from
both a positive and normative perspective: a lack of stationarity in preferences as implied
by endowment effects suggests that much of neoclassical theory is in need of revision.
In this paper, we provide a different explanation for the WTP/WTA disparity—a dynamic neoclassical theory based on the presence of commitment costs. Our theory
predicts that if agents are uncertain about the net payoff of a selling or purchasing transaction, and if they can obtain more information in the future, they will demand
compensation to trade now (thereby giving up the option to trade at a later time with
more information). WTP equals the good’s intrinsic value minus its associated compensation, and WTA equals intrinsic value plus its compensation. Thus, the divergence can
arise when the compensation, called commitment costs, exists and is consistent with
stable preferences and optimizing behavior on the part of agents. The disparity therefore
can be a logical outcome of optimizing behavior in a dynamic and stochastic setting.
If commitment costs are the primary sources of the disparity, then the basket of tools
associated with Hicksian welfare measurement can be fundamentally preserved, albeit
2 / Kling, List, and Zhao
with additional care given to the presence and interpretation of commitment costs and
their welfare effects. We explore the predictive power of our theory by examining WTP
and WTA statements of value from consumers behaving in a competitive marketplace:
the sportscard market. The sportscard marketplace is a natural setting for an examination
of preference structures, as it provides a rich pool of subjects making decisions in a
familiar environment, with uncertainty and future information about the values of the
traded good.
The empirical results are sharp. First, our data suggest that a disparity exists, even for
those consumers who plan to purchase the good for resale. Second, we find that the
comparative static predictions of the commitment cost theory perform quite well: WTP
(WTA) increases (decreases) in the difficulty of delay and decreases (increases) in the
difficulty of reversing the transaction. Further, the observed WTP/WTA divergence can,
in part, be attributable to the asymmetries in the perceived reversal and delay difficulties
between the buyers and sellers. We believe that this study is the first to document that a
neoclassical-based theory can explain the causes and severity of the value disparity.
Theoretical Background
Zhao and Kling (2001) presented an explicitly dynamic theory of the formation of
WTP and WTA and commitment costs under uncertainty and future learning. In this
section, we extend that model to the important setting of actual market experiments. We
show the conditions needed for commitment costs to arise and use these conditions to
design tests for the presence of commitment costs.
Consider a situation in which subjects formulate their WTP or WTA facing a trading
opportunity in an experiment, knowing that the same good (or a reasonable substitute)
can be traded outside in a “regular” market. Let v ∈ [vl , vh ] be their own (uncertain)
valuation of the good (hereafter “sportscard” or “card”), and let R ∈ [ Rl , Rh ] be their
information about the market price of the card. That is, they do not know v or R with
certainty but know their distributions. For simplicity, we assume that they can learn both
v and R with certainty later (i.e., after the experiment).2
Now, consider an experiment in which subjects can purchase the cards. If the subjects decide to purchase the card in the experiment but later (after learning v and R)
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 3
decide the card is not worth keeping, they can sell it at the realized market price, R .
However, doing so incurs a transaction cost c rp , where subscript p denotes WTP, and
superscript r denotes “reversing the trade.” In contrast, if they decide not to buy the card
in the experiment, they can purchase it later in the regular market, paying the market
price R while incurring a transaction cost c dp , where the superscript d denotes “delay.” In
experiments where subjects can sell the cards, let c Ar and c Ad be the transaction costs of
reversing the transaction (or buying the card back in the regular market) and delaying the
decision (or selling the card later in the market).
Formulation of WTP and WTA
Subjects’ WTP is defined as the maximum price they are willing to pay to buy the
card in the experiment, knowing that they can later learn about their valuation v and the
market price R. Suppose they buy at price P; if after the experiment the subjects’ realized
value of the card v is lower than R − cPr , they can sell the card and realize the gain of
R − cPr − v . Thus their expected payoff of buying at price p in the experiment is
U1 = E (v) + Ev < R −cr ( R − cPr − v) − p ,
(1)
P
where the second expectation is taken over both v and R in the region v < R − cPr and
represents the option value of reversing the purchasing transaction. To facilitate discussion, we denote this option value by OPr , or
OPr = Ev < R −c r ( R − cPr − v) .
(2)
P
If subjects delay or decline to purchase at price p, they still have the option of buying
the card later. They will then gain v but will pay the market price R plus the transaction
cost cPd . Thus their expected payoff is
U 2 = OPd ≡ Ev > R + cd (v − R − cPd ) ,
P
(3)
4 / Kling, List, and Zhao
where the expectation again is taken over the region v > R + cPd , and OPd denotes the
option value of buying the card later.
Subjects’ WTP is the unique p that equates U1 and U 2 . Hence,
WTP = E (v) − (OPd − OPr ) = E (v) + Ev< R −cr ( R − cPr − v) − Ev > R + c d (v − R − cPd ).
P
(4)
P
The term O pd − O pr is the commitment cost, representing the net loss of option values in
committing to the purchase now. Notice that WTP can be higher or lower than E(v), the
expected value of the card, depending on the value of the two options and thus the sign of
the commitment cost. If agents expect that the cost of reversing cPr is high but the cost of
delaying cPd is low, then OPr is low and OPd is high, yielding WTP < E (v) . If cPr = cPd , and
the random value R – v (the negative of the consumer surplus) is symmetric around zero,
then we expect the two option values to be equivalent, and WTP = E (v) . Equation (4)
also suggests that WTP should be increasing in the cost of delay c dp but decreasing in the
cost of reversal c rp .
The formation of WTA follows similar logic: subjects’ WTA is defined as the minimum price subjects are willing to accept to give up the card in the experiment. Suppose
subjects sell the card at price P. They still have the option of buying the card back in the
regular market (i.e., reversing their trade) at the market price R plus the transaction cost
c Ar , the value of which is denoted as OAr . Thus, their expected payoff is
π 1 = P + OAr − E (v) = P + Ev > R + c (v − R − c Ar ) − E (v) .
r
A
(5)
If they do not sell the card during the experiment, they retain the opportunity to sell
at the market price, incurring transaction cost c Ad . Thus, their expected payoff is
π 2 = OAd = Ev < R −c ( R − c Ad − v) ,
d
A
where OAd denotes the option value of selling the card later.
Again, equating π 1 and π 2 , we obtain WTA as
(6)
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 5
WTA = E (v) + OAd − OAr = E (v) + Ev< R −cd ( R − c Ad − v) − Ev > R + c r (v − R − c Ar ) ,
A
(7)
A
and OAd − OAr is the associated commitment cost. Similar to WTP, WTA can be below or
above E(v), depending on the magnitude of OAd and OAr . If subjects expect that there is a
small cost of delaying the transaction but a high cost of reversing it, or c Ad is small and
c Ar is high, OAd is high and OAr is low, leading to WTA > E (v ). Further, WTA is increasing in the cost of reversal c Ar but decreasing in the cost of delay c Ad .
WTP/WTA Divergence
From (4) and (7), we know that
WTA − WTP = (OAd − OAr ) + (OPd − OPr ) .
(8)
Therefore, the divergence between WTP and WTA equals the sum of the two commitment
costs. Further, WTA > WTP if at least one of the commitment costs is (sufficiently)
positive. If subjects believe that reversing a transaction is more costly than conducting the
transaction, regardless of whether they are thinking about buying or selling, we would
expect O Ad > O Ar and OPd > OPr , and thus WTA > WTP. Notice, however, that reversing the
selling decision is similar to delaying the buying decision: both involve buying the card
later. In this case, we may have c Ar = cPd . Similarly, reversing the purchasing decision is
similar to delaying the selling decision: both involve selling the card on the regular market.
Then, we may have cPr = c Ad . In this case, O Ad = OPr and OPd = OAr , and thus WTP = WTA.
Experiment Design and Hypotheses
Our objectives in designing the field experiment were twofold: (i) to investigate
whether subjects behave dynamically in forming their WTP and/or WTA values; that is,
whether they take potential opportunities for delay or reversal into account when forming
their bids or offers; and (ii) to examine whether conditions exist such that the dynamic
formulation can explain the WTP/WTA divergence. Two distinct field experiments were
undertaken to explore these issues. The first experiment uses data on subjects’ perception
of how difficult it would be to delay or reverse the proposed transactions. The second
6 / Kling, List, and Zhao
experiment exogenously varies the degree of delay and reversal difficulties associated
with the formation of WTA.
Field Experiment I: Perceptions Treatments
The first set of field treatments was carried out on the floor of a sportscard show in a
large eastern city. In both treatments (WTP and WTA), the experience of the subjects
typically followed four steps: (i) inspection of the card and learning the auction rules, (ii)
actual bid (offer), (iii) survey completion, and (iv) debriefing. In step 1 of the WTP
treatment, potential subjects approached the experimenter’s table and inquired about the
sale of the baseball card displayed on the table. For both treatment types, we chose a Cal
Ripken, Jr. 1983 Topps baseball card, which has a book value of approximately $12.
Both treatments displayed the same sportscard to all bidders—a Cal Ripken, Jr. PSA
graded as “PSA 8 near mint/mint” baseball card. This particular choice of a good was
appropriate as we conjectured that there would be a mix of subjects in this pool that
would opt to sell or trade the card if they left the experiment with the card.
The experimenter then invited potential subjects to take about five minutes to participate in an auction. If the subjects agreed, in step 2 the monitor explained the rules of
the random nth-price auction. As described in List and Shogren (1998), the random nthprice auction can be characterized by four simple steps: (i) each bidder submits a bid
(offer); (ii) each bid (offer) is rank-ordered from lowest to highest; (iii) the monitor
selects a random number (n) uniformly distributed between 2 and Z (Z bidders); and (iv)
in the WTP case, the monitor sells one unit of the good to each of the (n – 1) highest
bidders at the nth-price. In the WTA case, the monitor buys one unit each from the (n – 1)
lowest bidders and pays the nth-lowest bid. The monitor informed participants that their
bids would not be opened until after the show and that all bids would be destroyed when
the research project was completed. In the WTA treatment, after physically giving
subjects the card, the subjects made their offer.3
In step 3, the monitor asked the subjects to complete a confidential survey that would
be used for “statistical purposes only.” The survey, which is contained in the Appendix,
was used to obtain important information about what subjects planned to do with the card
if they won the auction (WTP) or did not sell in the auction (WTA). The choices included
“keep,” “trade,” or “sell.” The survey also obtained information about subjects’ percep-
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 7
tions of such things as ease of trade or sale or ease of purchase. In the fourth stage of the
experiment, the monitor explained to participants that they would be contacted within
three days after the show if they were among the n – 1 highest (lowest) bidders (offerers).
Subject were further informed that winners would receive the sheet after they had sent a
check or money order for the amount of the nth highest bid. The random n chosen was 24
for the WTP treatment and 30 for the WTA treatment. Within three days, the winners of
each auction were notified by phone or e-mail, and when the monitor received the check
(card), he mailed out the card (check).
Field Experiment II: Exogenous Treatments
The second set of field treatments was also carried out on the floor of a sportscard
show in a large eastern city. The same basic procedures were followed as described for
the first set of treatments, with several key differences. First, instead of using a
sportscard, we used an unopened pack of sportscards as the good. The pack of sportscards
had a retail value of approximately $3 and had been introduced recently to the market,
providing a sense of value uncertainty. Second, only WTA values were elicited and there
were three distinct treatments, which differed by the degree to which the monitor offered to
make reversal or delay of the transaction easier for subjects. The first treatment serves as a
control and links these results to the perceptions treatments in that subjects simply were
given the pack of sportscards and were asked to state their minimum WTA in an auction.
In the second treatment, subjects were informed that if they sold their pack at the
auction, they would be allowed to return the following week and repurchase the pack
from the monitor at the selling price (or upon receipt of payment the monitor would mail
the pack, postage paid). We denote this treatment as the “goods-back-guarantee” (GBG)
treatment; it is designed to reduce the cost to the subject of reversing a transaction, should
the subject wish to do so.
In the third treatment, subjects were informed that if they did not sell their pack at
the auction, they could return the following week and use space on the monitor’s dealer
table to attempt to sell the pack. We term this treatment the “table” treatment; it is
designed to reduce the cost to the subject of delaying the transaction.
8 / Kling, List, and Zhao
Hypotheses
With these field data, we are able to test two types of hypotheses. First, we examine
whether subjects form their WTP and WTA values dynamically:
HYPOTHESIS 1: WTP (WTA) increases (decreases) in the delay difficulty cPd ( c Ad ) and
decreases (increases) in the reversal difficulty cPr ( c Ar ).
In the first field experiment, we test this hypothesis in terms of the perceived delay and
reversal difficulties. In the second field experiment, we study the effects of both the
perceived and actual delay and reversal difficulties.
Second, we test whether the observed WTP/WTA values relate to the delay and reversal difficulties:
HYPOTHESIS 2: (i) WTA>WTP if subjects in both WTP and WTA treatments perceive
that it is more difficult to reverse than to delay the respective transaction: cPr > cPd
and cAr > c Ad ; (ii) WTA<WTP if subjects in both treatments perceive that it is easier
to reverse than to delay the respective transactions: cPr < cPd and cAr < c Ad ; (iii)
WTA=WTP if subjects perceive the same selling (or buying) difficulties across the
WTP and WTA transactions: cPr = c Ad and cPd = c Ar .
Here, only the first set of field treatments is relevant, as data on both WTP and WTA are
necessary, and perceptions of the delay and reversal difficulties are critical to the predictions. Note that even if the respondents behave according to the commitment cost theory,
WTA is greater than WTP only when the perceived delay and reversal difficulties satisfy
certain conditions. Otherwise, it is possible that WTA is less than or equal to WTP.
Experiment Results
Table 1 summarizes the relevant statistics from field experiment I. Column 1 contains summary statistics for the overall sample, while columns 2 and 3 contain
information for the WTP and WTA subsamples. Data in the first row suggest that the
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 9
TABLE 1. Summary statistics: field experiment I
Variable
Bid/offer value
Value for keepers
Value for non-keepers
Years experience
Dealer
Gender
Age
Education
Keep
Delay difficulty
Delay difficulty for
keepers
Delay difficulty for nonkeepers
Purchase
Reversal difficulty
Reversal difficulty for
keepers
Reversal difficulty for
non-keepers
Income
Outcome
Market value
Total Sample
9.69 (90)
[6.74]
–
–
8.42 (90)
[5.50]
0.11 (90)
[0.32]
0.90 (90)
[0.31]
34.61 (90)
[11.48]
15.18 (90)
[15.17]
0.37 (90)
[0.37]
1.68 (72)
[0.82]
–
–
2.22 (90)
[0.91]
1.95 (75)
[1.01]
–
–
53,765 (83)
[26,154]
2.26 (41)
[2.27]
12.69 (81)
[7.20]
WTP
Subsample
7.46 (49)
[4.64]
7.00 (15)
[3.89]
7.67 (34)
[4.97]
8.27 (49)
[6.03]
0.14 (49)
[0.36]
0.92 (49)
[0.28]
33.47 (49)
[11.41]
15.06 (49)
[3.22]
0.31 (49)
[0.47]
1.55 (49)
[0.74]
1.20 (15)
[0.41]
1.71 (34)
[0.80]
1.92 (49)
[0.99]
2.41 (34)
[1.10]
–
2.41(34)
[1.10]
55,640 (43)
[22,827]
2.27 (49)
[0.95]
14.46 (45)
[7.56]
WTA
Subsample
12.37 (41)
[7.35]
15.39 (18)
[8.07]
10.00 (23)
[5.89]
8.61 (41)
[4.87]
0.07 (41)
[0.26]
0.88 (41)
[0.33]
35.98 (41)
[11.56]
15.32 (41)
[2.55]
0.44 (41)
[0.50]
1.96 (23)
[0.92]
–
1.96 (23)
[0.93]
2.59 (41)
[0.63]
1.56 (41)
[0.74]
1.56 (18)
[0.86]
1.57 (23)
[0.66]
51,750 (40)
[23,137]
na
10.47 (36)
[6.13]
Note: The table presents the sample means of the variables, with the number of sample points in
parentheses and the standard deviations in square brackets.
10 / Kling, List, and Zhao
average WTA ($12.37) is much larger than the average WTP ($7.46), and this difference is statistically significant.4 Thus, the value divergence commonly found in the
literature certainly is present in experiment I as well.
Data presented in rows 2 and 3 push the analysis a level deeper and suggest that
WTA and WTP subjects who plan to keep the card behave differently from one another; average WTA values ($15.39) are much larger than comparable WTP values
($7.00), and this difference is statistically significant at conventional levels. Yet even
for those who plan to trade/sell the card, a nontrivial value disparity exists: WTP =
$7.67 versus WTA = $10.00. This difference is only statistically significant at the
p < 0.054 level using a one-sided alternative, however. This result is inconsistent with,
for example, theories that suggest that indifference curves are unstable across different
property rights regimes. A key feature of these theories is that value disparities should
not be present when the individual views the good only as a medium of exchange. As
Kahneman, Knetsch, and Thaler (1990, p. 1328) note, “there are some cases in which
no endowment effect would be expected, such as when goods are purchased for resale
rather than for utilization.”5
Table 2 summarizes the relevant statistics for experiment II, which was designed
with treatments that exogenously varied the delay and reversal difficulties in WTA.
The reversal cost c Ar is reduced in the GBG treatment, and the delay cost c Ad is reduced
in the table treatment. Subjects’ perceptions of the delay and reversal costs are elicited
through a survey instrument, as in experiment I.
Table 2 also contains the mean offer values for “keepers,” who indicated that they
expected to keep their pack if they did not sell it in the auction, as well as average
values for “non-keepers,” who intend to sell or trade at a later date if they are unsuccessful in the auction. These average values qualitatively mimic those in Table 1. In all
cases, keepers report a higher average WTA. Further, they perceive that it is harder to
reverse the trade and easier to delay selling the pack than do non-keepers. This asymmetric perception about the ease of delay and reversal is consistent with a higher WTA
value for keepers, based on the commitment cost theory.
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 11
TABLE 2. Summary statistics: field experiment II
Base
Variable
Total Sample
Subsample
WTA value
4.10 (112)
4.66 (55)
[2.29]
[2.18]
Value for keepers
4.60 (27)
4.69 (13)
[2.46]
[2.09]
Value for
3.48 (23)
3.62 (12)
non-keepers
[1.55]
[1.72]
Years experience
11.74 (112)
12.76 (55)
[10.37]
[12.60]
Dealer
0.10 (112)
0.16 (55)
[0.30]
[0.37]
Gender
0.875 (112)
0.87 (55)
[0.33]
[0.31]
Age
38.58 (112)
39.6 (55)
[13.52]
[14.79]
Education
15.05 (112)
15.09 (55)
[2.46]
[2.40]
Keep
0.54 (50)
0.52 (25)
[0.50]
[0.51]
3.12 (41)
3.04 (24)
Delay difficultya
[1.38]
[1.20]
Delay difficulty for
2.88 (24)
2.92 (13)
keepers
[1.42]
[1.32]
Delay difficulty for
3.47 (17)
3.18 (11)
non-keepers
[1.28]
[1.08]
Reversal difficulty
1.77 (89)
1.86 (43)
[0.88]
[0.94]
Reversal difficulty
2.11 (27)
2.31 (13)
for keepers
[0.93]
[1.11]
Reversal difficulty
1.52(23)
1.58 (12)
for non-keepers
[0.73]
[0.67]
Income
Market value
59,085 (112)
[30,657]
4.49 (112)
[2.15]
54,545 (55)
[30,112]
4.98 (55)
[2.31]
GBG
Subsample
3.23 (32)
[2.18]
–
–
10.62 (32)
[7.96]
0.00(32)
[0.00]
0.88 (32)
[0.34]
36.75 (32)
[12.61]
15.06 (32)
[2.82]
–
–
–
–
1.67 (21)
[0.87]
–
–
68,672 (32)
[30,848]
4.24 (32)
[2.08]
Table
Subsample
3.98 (25)
[2.36]
4.50 (14)
2.84
3.32 (11)
[1.42]
8.61 (41)
[4.87]
0.08 (25)
[0.26]
0.88 (25)
[0.33]
38.68 (25)
[11.89]
14.96 (25)
[2.17]
0.56 (25)
[0.51]
3.24 (17)
[1.64]
2.82 (11)
[1.60]
4.00(6)
[1.55]
1.72 (25)
[0.79]
1.93 (14)
[0.73]
1.45 (11)
[0.82]
58,800 (25)
[30.04]
3.51 (25)
[1.54]
Note: The table presents the sample means of the variables, with the number of sample points in
parentheses and the standard deviations in square brackets.
a
Delay difficulty and intent to keep was collected only for the “table treatment” subsample and corresponding base subsample as explained in the text.
12 / Kling, List, and Zhao
Hypothesis 1
Using data from experiment I, we run a series of simple ordinary least squares (OLS)
bid/offer regressions. Tables 3 and 4 present the estimation results for six specifications
for WTP (WTA), where the dependent variables are the individual bids (offers). Specifications 1 and 2 estimate the effects of the difficulties of delaying and reversing the
transaction on the WTP and WTA values; specifications 3 and 4 estimate the effects of
being a keeper; and specifications 5 and 6 combine these models.6
The regression results strongly support our theoretical predictions: reversal difficulty
and delay difficulty are statistically significant at conventional levels, and their signs are
consistent with predictions of the commitment cost theory for both WTP and WTA and
consistent across the specifications. For example, reversal difficulty reduces WTP and
increases WTA, while delay difficulty reduces WTA and increases WTP.
In experiment II, as shown in Table 2, the mean reported WTA for those with GBG
is $3.23, which is statistically different from WTA of the control group ($4.66). Since a
GBG reduces the reversal difficulty, this result is consistent with Hypothesis 1. Results
for the table treatment subsample are directionally consistent with Hypothesis 1, but the
mean WTA of $3.98 is not significantly different from $3.23 at conventional levels.
TABLE 3. Willingness-to-pay regressions: experiment I
Specifications
1
2
3
4
Constant
7.75**
8.39**
7.66**
7.69**
(3.27)
(3.08)
(9.56)
(8.45)
Reversal
-1.82**
-1.93**
difficultya
(-2.75)
(-2.73)
Delay
2.52**
2.42**
b
(2.76)
(2.57)
difficulty
Keep
-0.66
-0.69
(=1 if keep)
(-0.46)
(-0.45)
Dealer
-0.97
-0.11
(=1 if a dealer)
(-0.50)
(-0.06)
Gender
(=1 if male)
R2
N
0.34
34
0.34
34
0.00
49
0.06
49
5
6.37*
(1.92)
6
6.12*
(1.75)
1.90*
(1.93)
0.56
(0.38)
-2.21
(-0.87)
1.95*
(1.92)
0.68
(0.44)
0.50
(0.26)
-2.15
(-0.84)
0.13
49
0.13
49
Note: Numbers in parentheses are t-statistics. * significant at 10%; ** significant at 5%.
a
Response to question 10b.
b
Response to question 11a.
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 13
TABLE 4. Willingness-to-accept regressions: experiment I
Specifications
1
2
3
4
Constant
12.55**
14.10** 10.00**
9.85**
(3.24)
(3.08)
(6.93)
(6.29)
Reversal
2.38
2.08
difficultya
(1.49)
(1.23)
Delay
-3.21**
-3.61**
b
difficulty
(-2.82)
(-2.76)
Keep
5.39**
5.54**
(=1 if keep)
(2.47)
(2.43)
Dealer
-2.26
1.15
(=1 if a dealer)
(-0.66)
(0.26)
Gender
(=1 if male)
R2
N
0.40
23
0.41
23
0.14
41
0.09
41
5
5.00
(1.29)
4.40**
(3.31)
6
4.73
(1.20)
4.47**
(3.33)
5.47**
(2.85)
-2.18
(-0.73)
5.83**
(2.92)
2.70
(0.70)
-2.38
(-0.79)
0.36
41
0.37
41
Note: Numbers in parentheses are t-statistics. * significant at 10%; ** significant at 5%.
a
Response to question 11a (note that this is different from the WTP table).
b
Response to question 10b.
As in experiment I, we run a set of OLS regressions and report summary estimates in
Table 5. Table 5 includes a series of specifications that generally provides insights
consonant with Hypothesis 1. For example, in specification 1, while the table treatment
dummy variable is not significant at conventional levels, the GBG dummy is highly
significant and negative, consistent with Hypothesis 1. In addition, empirical results in
columns 2 and 3 show that the coefficient of reversal difficulty is positive and highly
significant. Specifications 4 and 5 provide insights on the robustness of the statistical
significance of the treatment dummies with respect to the dealer and gender variables. In
each case, the GBG dummy variable remains highly significant and negative. Specifications in columns 6–8 report regression results using models that include delay difficulty
and whether subjects planned to keep the good.7 Neither the perceived delay difficulty
nor the table treatment dummy is statistically significant at conventional levels. However,
the perceived reversal difficulty is statistically significant, and its sign is consistent with
Hypothesis 1.8
0.07
112
0.21
89
2
2.85**
(5.12)
-1.60 **
(-2.94)
-0.38
(-0.74)
0.88**
(3.53)
0.25
89
1.29*
(1.92)
3
2.57**
(4.54)
-1.33**
(-2.40)
-0.21
(-0.41)
0.88**
(0.25)
0.09
112
1.04
(1.45)
0.09
112
1.00
(1.37)
0.27
(0.43)
Specifications
4
5
4.49*
4.26**
(14.01)
(6.75)
-1.26**
-1.27 **
(-2.49)
(-2.49)
-0.59
-0.60
(-1.11)
(-1.11)
Note: Numbers in parentheses are t-statistics. * significant at 10%; ** significant at 5%.
a
Response to question 11a.
b
Response to question 10b.
R2
N
Reversal
difficultya
Delay
difficultyb
Keep
(=1 if keep)
Dealer
(=1 if a dealer)
Gender
(=1 if male)
Table dummy
GBG dummy
Constant
1
4.66**
(15.56)
-1.43**
(-2.89)
-0.68
(-1.27)
TABLE 5. Willingness-to-accept regressions: experiment II
0.00
50
-0.20
(-0.33)
6
4.18**
(9.63)
0.07
50
1.12*
(1.87)
-0.24
(-0.41)
7
3.60**
(6.84)
0.29
41
0.45
(0.68)
1.16**
(2.85)
-0.35
(-1.51)
0.05
(0.67)
8
3.05*
(2.51)
14 / Kling, List, and Zhao
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 15
Hypothesis 2
We return to the experiment I data to examine the WTP and WTA values for various
combinations of the perceived delay/reversal difficulties. Table 6 groups the subjects into
the three categories specified in Hypothesis 2. Data summarized in row 1 support Hypothesis 2(i): the average WTA of 13.33 is larger than the average WTP of 5.84 for those
who perceive a higher reversal difficulty than delay difficulty, and the difference is
significant. Row 3 of Table 6 confirms Hypothesis 2(ii): WTP (13.93) > WTA (6.25) for
the case of reversal difficulty being smaller than the delay difficulty. Again, the difference is statistically significant at conventional levels. We find this result to be quite
amazing, as it suggests the strength of our dynamic option-based theory—aligning groups
of subjects by the degree of delay/reversal difficulty yields average WTP values that are
greater than average WTA values, precisely as the commitment cost theory predicts.
Several pieces of evidence from Table 6 are relevant for Hypothesis 2(iii). First, for
subjects who perceive a higher difficulty to sell than to buy in both WTP and WTA,
average WTP (5.84) is not significantly different from the average WTA (6.25). For those
perceiving a higher difficulty to buy, average WTP (13.93) is not statistically different
from the average WTA (13.33). Both null results are consistent with Hypothesis 2(iii).
Yet results summarized in row 2 of Table 6 do not confirm 2(iii): although our theory
predicts WTP = WTA when the delay and reversal costs are equivalent, the data indicate
WTA > WTP. This result is, however, consistent with Hanemann’s (1991) neoclassical
explanation: because of income (shifts in the indifference curve) and substitution (curvature of the indifference curves) effects, neoclassical theory predicts value divergences.
TABLE 6. Effects of relative reversal and delay difficulties: experiment I
Relative Difficulties
1. Reversal difficulty > delay difficulty
2. Reversal difficulty = delay difficulty
3. Reversal difficulty < delay difficulty
Note: Numbers in parentheses are standard deviations.
WTP
Mean
N
5.84
19
(3.11)
6.50
8
(4.07)
13.93
7
(5.42)
WTA
Mean
N
13.33
6
(5.47)
15.00
5
(6.12)
6.25
12
(3.05)
16 / Kling, List, and Zhao
Table 7 makes a finer split of the data by comparing specific levels of reversal/delay
difficulties. Each cell represents WTP and WTA values for subjects who perceived
certain degrees of buying and selling difficulties. For Hypothesis 2(i), the relevant
comparisons are the WTP values in cells below the diagonal and WTA values in cells
above the diagonal. These are subjects who perceive a higher reversal difficulty than
delay difficulty in both WTP and WTA transactions. In these data it is clear that WTA>
WTP either in pair-wise comparisons or in aggregate, supporting Hypothesis 2(i).
Similarly, Hypothesis 2(ii) is confirmed by a comparison of the WTP values in cells
above the diagonal with WTA values in cells below the diagonal. Further, since the WTP
and WTA values in the same cell are formed under beliefs about selling and buying difficulties that are consistent across the WTP and WTA treatments, Hypothesis 2(iii) predicts
that the two values should be equivalent in each cell. Among the eight cells for which both
values are reported, the average WTP is similar to the average WTA in six cells (WTA is
higher than WTP in the other two cells). This observation supports Hypothesis 2(iii).9
Concluding Remarks
The divergence of compensation demanded and WTP measures of value has
prompted many economists to pause and contemplate whether the basic tenets of neoclassical theory are satisfied. Some commentators have used the vast empirical evidence to
TABLE 7. Perceptions of reversal/delay difficulties: experiment I
Difficulty of
selling
later
(RevD for
WTP, or
DelayD for
WTA)
1
2
3
4
5
Difficulty of buying later (DelayD for WTP, or RevD for WTA)
1
2
3
4
5
3.50 (2)
16 (3)
15 (1)
13.33 (3)
13 (4)
14 (2)
6.8 (5)
9.0 (5)
12.5 (2)
9.5 (1)
7.4 (5)
17.5 (2)
–
–
5.50 (6)
8.33 (3)
4.25 (4)
9.00 (2)
4 (2)
5 (1)
–
3 (1)
5 (1)
1 (1)
–
–
Note: The first entry is the average WTP, and the bottom entry is the average WTA; the sample size is in
parentheses.
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 17
call into question the fundamental building blocks of economic theory. While static
neoclassical theories have been proposed to explain the observed preferences, the data
generally have not conformed well to these theories. In this paper, we examine whether a
dynamic neoclassical theory based on the presence of commitment costs can explain the
behavior of individuals within a competitive marketplace.
We find several pieces of evidence that are in favor of the commitment cost theory.
First, our field experiment results suggest that a value disparity exists, even for those
consumers who plan to purchase the good for resale. Second, we find that the comparative static predictions of the theory perform quite well: WTP (compensation demanded)
increases (decreases) in the difficulty of delay and decreases (increases) in the difficulty
of reversing the transaction. Third, even under the most stringent of our theoretical
conjectures—including cases where WTP is predicted to exceed WTA—our data perform
well. Overall, our results suggest that commitment costs are an important source of the
value disparity and provide strong evidence that a neoclassical-based theory can explain
the causes and severity of the value disparity.
Endnotes
1.
Hanemann’s (1991) work extended that of Randall and Stoll (1980), who demonstrated that the WTP/WTA disparity depends on the “price flexibility of income.”
Hanemann proved that the price flexibility of income is analytically equivalent to the
ratio of the ordinary income elasticity of demand for the good to the Allen-Uzawa
elasticity of substitution between the good and the numéraire. Thus, for low elasticity of substitution values, the price flexibility of income is large, suggesting that the
ratio WTP/WTA also is large.
2.
This assumption can be relaxed without changing the key results of our model. If the
uncertainty is only partially resolved, the magnitude of the commitment cost effect
will be smaller than if the resolution is complete, but the qualitative results will remain unchanged.
3.
We should also note that we randomized participants into one of the two treatments
by changing the treatment type at the top of each hour. Also, subjects only participated in one treatment.
4.
Unless otherwise noted, all claims are supported by statistical tests at the 5 percent
level. For every unconditional comparison, we employ a two-sample t-test and a
two-sample Wilcoxon rank-sum test.
5.
Average values of the subject-specific characteristics are similar across the two
subsamples, indicating that our experiment procedure was successful at random
placement of subjects in the two treatments.
6.
Since “keepers” only answered the question of purchasing the good in the future,
only delay difficulty is included for WTP and only reversal difficulty is included for
WTA in specifications 5 and 6.
7.
The number of observations decreases considerably in these specifications because
many subjects left responses to these questions blank. Also, the GBG treatment
dummy is not identifiable since none of these subjects completed the “delay difficulty” and “keep” questions because of experiment error.
8.
Overall, in experiment II, the effects of the GBG and the perceived reversal difficulty
provide perspicuous support for Hypothesis 1, but the table treatment and the perceived delay difficulty variables are consistently insignificant. There are at least two
possible explanations. One is that respondents did not view the offer to use the monitor’s table the next week as a significant decrease in the cost of delaying their
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 19
transaction to notably lower their commitment costs (they would still have to take the
time to come and use the table with an uncertain outcome). Alternatively, respondents
may not have been considering the delay possibility when forming their WTA values.
9.
Our theory also conveniently describes empirical results that suggest that market
experience attenuates the value disparity (e.g., Knez, Smith, and Williams 1985;
Coursey, Hovis, and Schulze 1987; Brookshire and Coursey 1987; List 2003).
Appendix
Survey Forms
(I) WTP Treatment
Confidential Survey
These questions will be used for statistical purposes only. THIS INFORMATION WILL
BE KEPT CONFIDENTIAL AND WILL BE DESTROYED UPON COMPLETION
OF THE STUDY.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
How long have you been active in the sportscard and memorabilia market? ______yrs
Are you a sportscard or sports memorabilia professional dealer? ________
How many sportscard or memorabilia shows do you attend in a typical year? _______
In how many of those do you typically trade? ___________
Gender: 1) Male 2) Female
Age ______
Date of Birth ____________
What is the highest grade of education that you have completed. (Circle one)
1) Eighth grade 3) 2-Year College
5) 4-Year College
2) High School 4) Other Post-High School 6) Graduate School Education
What is your approximate yearly income from all sources, before taxes?
1) Less than $10,000
5) $40,000 to $49,999
2) $10,000 to $19,999 6) $50,000 to $74,999
3) $20,000 to $29,999 7) $75,000 to $99,999
4) $30,000 to $39,999 8) $100,000 or over
What do you think is the likely market value of the good (a range is fine)?________
If you win the auction:
A. What do you plan to do with the good? Sell it ____ Trade it ____ Keep it _____
B. If you plan to sell/trade the good, how easy do you think it will be to sell/trade?
1 (very easy)
2
3
4
5 (almost impossible)
C. If you decide to sell the good, which of the following do you think is true? You could
(a) Recoup the full bid_____
(b) Take a loss ______
(c) Earn a profit ______
If you do not win the auction:
A. How easy do you think it will be to obtain the good (or a close substitute) later?
1 (very easy)
2
3
4
5 (almost impossible)
The WTP/WTA Disparity: Have We Been Observing Dynamic Values but Interpreting Them as Static? / 21
B. If you were to purchase the good (or a close substitute) later, which of the following
do you think is true? The purchase price would be
(a) Above my bid ______
(b) Below my bid ______
(c) About the same as my bid _____
(II) WTA Treatment
Confidential Survey
These questions will be used for statistical purposes only. THIS INFORMATION WILL
BE KEPT CONFIDENTIAL AND WILL BE DESTROYED UPON COMPLETION
OF THE STUDY.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
How long have you been active in the sportscard and memorabilia market? ______yrs
Are you a sportscard or sports memorabilia professional dealer? ________
How many sportscard or memorabilia shows do you attend in a typical year? _______
In how many of those do you typically trade? ___________
Gender: 1) Male 2) Female
Age ______
Date of Birth ____________
What is the highest grade of education that you have completed. (Circle one)
1) Eighth grade 3) 2-Year College
5) 4-Year College
2) High School 4) Other Post-High School 6) Graduate School Education
What is your approximate yearly income from all sources, before taxes?
1) Less than $10,000
5) $40,000 to $49,999
2) $10,000 to $19,999 6) $50,000 to $74,999
3) $20,000 to $29,999 7) $75,000 to $99,999
4) $30,000 to $39,999 8) $100,000 or over
What do you think is the likely market value of the good (a range is fine)?________
If you do not sell in the auction:
A. What do you plan to do with the good? Sell it ____ Trade it ____ Keep it _____
B. If you plan to sell/trade the good, how easy do you think it will be to sell/trade?
1 (very easy) 2
3
4
5 (almost impossible)
If you do sell the good in the auction:
A. How easy do you think it will be to obtain the good (or a close substitute) later?
1 (very easy) 2
3
4
5 (almost impossible)
B. If you were to purchase the good (or a close substitute) later, which of the following
do you think is true? The purchase price would be
Above my offer______
Below my offer______
About the same as my offer_____
References
Brookshire, David, and Don Coursey. 1987. “Measuring the Value of a Public Good: An Empirical
Comparison of Elicitation Procedures.” American Economic Review 77(4, September): 554-66.
Coursey, Don, John Hovis, and William Schulze. 1987. “The Disparity between Willingness to Accept and
Willingness to Pay Measures of Value.” Quarterly Journal of Economics 102(3): 679-90.
Hanemann, W. Michael. 1991. “Willingness to Pay and Willingness to Accept: How Much Can They
Differ?” American Economic Review June 81(3): 635-47.
Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler. 1990. “Experimental Tests of the Endowment
Effect and the Coase Theorem.” Journal of Political Economy 98: 1325-48.
Knez, Peter, Vernon L. Smith, and Arlington Williams. 1985. “Individual Rationality, Market Rationality,
and Value Estimation.” American Economic Review 75(2, May): 397-402.
List, John A. 2003. “Does Market Experience Eliminate Market Anomalies?” Quarterly Journal of
Economics 118(1): 41-71.
List, John A., and Jason F. Shogren. 1998. “The Deadweight Loss of Christmas: Comment.” American
Economic Review 88(5, December): 1350-55.
Randall, Alan, and John R. Stoll. 1980. “Consumer’s Surplus in Commodity Space.” American Economic
Review 71(3, June): 449-57.
Zhao, Jinhua, and Catherine Kling. 2001. “A New Explanation for the WTP/WTA Disparity.” Economics
Letters (73): 293-300.